Bayesian model reduction and empirical Bayes for group (DCM) studies

Karl J. Friston, Vladimir Litvak, Ashwini Oswal, Adeel Razi, Klaas E. Stephan, Bernadette C.M. Van Wijk, Gabriel Ziegler, Peter Zeidman

Research output: Contribution to journalArticleResearchpeer-review

149 Citations (Scopus)


This technical note describes some Bayesian procedures for the analysis of group studies that use nonlinear models at the first (within-subject) level - e.g., dynamic causal models - and linear models at subsequent (between-subject) levels. Its focus is on using Bayesian model reduction to finesse the inversion of multiple models of a single dataset or a single (hierarchical or empirical Bayes) model of multiple datasets. These applications of Bayesian model reduction allow one to consider parametric random effects and make inferences about group effects very efficiently (in a few seconds). We provide the relatively straightforward theoretical background to these procedures and illustrate their application using a worked example. This example uses a simulated mismatch negativity study of schizophrenia. We illustrate the robustness of Bayesian model reduction to violations of the (commonly used) Laplace assumption in dynamic causal modelling and show how its recursive application can facilitate both classical and Bayesian inference about group differences. Finally, we consider the application of these empirical Bayesian procedures to classification and prediction.

Original languageEnglish
Pages (from-to)413-431
Number of pages19
Publication statusPublished - 1 Mar 2016
Externally publishedYes


  • Bayesian model reduction
  • Classification
  • Dynamic causal modelling
  • Empirical Bayes
  • Fixed effects
  • Hierarchical modelling
  • Random effects

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